非均匀C-C细分曲面的曲率分析  

Curvature Analysis of the Non-uniform C-C Subdivision Surfaces

作　　者：刘浩[1] 廖文和[1] 张湘玉[1] 

机构地区：[1]南京航空航天大学机电学院,南京210016

出　　处：《机械科学与技术》2007年第12期1534-1539,共6页Mechanical Science and Technology for Aerospace Engineering

摘　　要：分析了非均匀C-C细分的特点,为细分网格上正则部分的曲率计算给出了两种方法:基于网格顶点的曲率计算和基于网格面的曲率计算。这两种方法都能精确计算出网格的正则点在极限位置的曲率。对于以面为基础的方法,还能精确计算出网格的正则面在极限曲面上对应区域的任意参数位置的曲率。这两种曲率计算的方法也能够精确计算出网格正则部分的其它几何属性,如法矢量、主方向、主曲率等。对于奇异点附近区域的曲率,本文给出的算例用局部逐层细分的方式进行逼近。细分曲面任意位置的几何属性都可能需要计算时,本文的方法可以作为解析法的补充。This paper analyses the properties of the non-uniform C-C subdivision and presents two methods for calculating curvatures at the regular regions on non-uniform C-C subdivision surfaces ： one is based on mesh vertex and the other based on mesh face. The two methods can all calculate exactly curvatures of limit positions of regular points of mesh. The method based on mesh face can also calculate exactly the curvature of any parameter positions of limit regions corresponding to regular faces of mesh. In addition to the curvature, the two methods can also calculate exactly other geometrical properties of points on non-uniform C-C subdivision surfaces such as normal vector, principal curvature and principal direction, etc. For curvatures at regions around the extraordinary points, the paper analyses the local progressive subdivision method and approaches curvatures at the regions around the extraordinary points. Curvature calculation methods in this paper can be treated as complementary to the analytic methods when geometrical properties of any positions on subdivision surfaces are probably needed.

关 键 词：非均匀C-C细分 曲面 曲率分析 

分 类 号：TP391.6[自动化与计算机技术—计算机应用技术]